Enhancement of the knapsack algorithm with memorization and generalisation

knapsack/README.md

@@ -1,4 +1,4 @@
-# A naive recursive implementation of 0-1 Knapsack Problem
+# A recursive implementation of 0-N Knapsack Problem
 
 This overview is taken from:
 

knapsack/knapsack.py

@@ -1,43 +1,68 @@
-""" A naive recursive implementation of 0-1 Knapsack Problem
+""" A recursive implementation of 0-N Knapsack Problem
     https://en.wikipedia.org/wiki/Knapsack_problem
 """
 from __future__ import annotations
 
+from functools import lru_cache
 
-def knapsack(capacity: int, weights: list[int], values: list[int], counter: int) -> int:
+
+def knapsack(
+    capacity: int,
+    weights: list[int],
+    values: list[int],
+    counter: int,
+    allow_repetition=False,
+) -> int:
     """
     Returns the maximum value that can be put in a knapsack of a capacity cap,
-    whereby each weight w has a specific value val.
+    whereby each weight w has a specific value val
+    with option to allow repetitive selection of items
 
     >>> cap = 50
     >>> val = [60, 100, 120]
     >>> w = [10, 20, 30]
     >>> c = len(val)
-    >>> knapsack(cap, w, val, c)
+    >>> knapsack(cap, w, val, c, False)
     220
 
-    The result is 220 cause the values of 100 and 120 got the weight of 50
+    Given the repetition is NOT allowed,
+    the result is 220 cause the values of 100 and 120 got the weight of 50
+    which is the limit of the capacity.
+    >>> knapsack(cap, w, val, c, True)
+    300
+
+    Given the repetition is allowed,
+    the result is 300 cause the values of 60*5 (pick 5 times)
     which is the limit of the capacity.
     """
 
-    # Base Case
-    if counter == 0 or capacity == 0:
-        return 0
-
-    # If weight of the nth item is more than Knapsack of capacity,
-    #   then this item cannot be included in the optimal solution,
-    # else return the maximum of two cases:
-    #   (1) nth item included
-    #   (2) not included
-    if weights[counter - 1] > capacity:
-        return knapsack(capacity, weights, values, counter - 1)
-    else:
-        left_capacity = capacity - weights[counter - 1]
-        new_value_included = values[counter - 1] + knapsack(
-            left_capacity, weights, values, counter - 1
-        )
-        without_new_value = knapsack(capacity, weights, values, counter - 1)
-        return max(new_value_included, without_new_value)
+    @lru_cache
+    def knapsack_recur(cap: int, c: int) -> int:
+        # Base Case
+        if c == 0 or cap == 0:
+            return 0
+
+        # If weight of the nth item is more than Knapsack of capacity,
+        #   then this item cannot be included in the optimal solution,
+        # else return the maximum of two cases:
+        #   (1) not included
+        #   (2) nth item included one or more times (0-N), if allow_repetition is true
+        #       nth item included only once (0-1), if allow_repetition is false
+        if weights[c - 1] > cap:
+            return knapsack_recur(cap, c - 1)
+        else:
+            without_new_value = knapsack_recur(cap, c - 1)
+            if allow_repetition:
+                new_value_included = values[c - 1] + knapsack_recur(
+                    cap - weights[c - 1], c
+                )
+            else:
+                new_value_included = values[c - 1] + knapsack_recur(
+                    cap - weights[c - 1], c - 1
+                )
+            return max(new_value_included, without_new_value)
+
+    return knapsack_recur(capacity, counter)
 
 
 if __name__ == "__main__":

knapsack/tests/test_knapsack.py

@@ -45,7 +45,17 @@ def test_knapsack(self):
         val = [60, 100, 120]
         w = [10, 20, 30]
         c = len(val)
-        self.assertEqual(k.knapsack(cap, w, val, c), 220)
+        self.assertEqual(k.knapsack(cap, w, val, c, False), 220)
+
+    def test_knapsack_repetition(self):
+        """
+        test for the knapsack
+        """
+        cap = 50
+        val = [60, 100, 120]
+        w = [10, 20, 30]
+        c = len(val)
+        self.assertEqual(k.knapsack(cap, w, val, c, True), 300)
 
 
 if __name__ == "__main__":